Упр.446 Часть 2 ГДЗ Дорофеев Петерсон 5 класс (Математика)

Задача

Составь программу действий и вычисли:

$$1+\frac{2}{1-\frac{1}{2}}$$
$$\frac{\frac{3}{\frac{1}{3}+1}-2}{1-\frac{3}{4}}$$
$$\frac{1+\frac{\frac{1}{3}-\frac{1}{5}}{2}}{1-\frac{\frac{1}{3}+\frac{1}{5}}{2}}$$
$$\frac{\frac{4}{\frac{1}{2}+\frac{1}{6}}-1\frac{1}{2}}{\frac{4}{\frac{1}{2}-\frac{1}{6}}+1\frac{1}{2}}$$
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}$$
$$2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac{1}{2}}}}$$

Подробный ответ

1) $$1+\frac{2}{1-\frac12}=1+\frac{2}{\frac12}=1+2\cdot 2=5.$$

2) $$\frac{\frac{3}{\frac13+1}-2}{1-\frac34}=\frac{\frac{3}{\frac43}-2}{\frac14}=\frac{\frac94-2}{\frac14}=\frac{\frac14}{\frac14}=1.$$

3) $$\frac{1+\frac{\frac13-\frac15}{2}}{1-\frac{\frac13+\frac15}{2}}=\frac{1+\frac{\frac{2}{15}}{2}}{1-\frac{\frac{8}{15}}{2}}=\frac{1+\frac{1}{15}}{1-\frac{4}{15}}=\frac{\frac{16}{15}}{\frac{11}{15}}=\frac{16}{11}=1\frac{5}{11}.$$

4) $$\frac{\frac{4}{\frac12+\frac16}-1\frac12}{\frac{4}{\frac12-\frac16}+1\frac12}=\frac{\frac{4}{\frac23}-1\frac12}{\frac{4}{\frac13}+1\frac12}=\frac{6-1\frac12}{12+1\frac12}=\frac{4\frac12}{13\frac12}=\frac{\frac92}{\frac{27}{2}}=\frac{9}{27}=\frac13.$$

5) $$1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac12}}}=1+\frac{1}{1+\frac{1}{1+\frac{1}{\frac32}}}=1+\frac{1}{1+\frac{1}{1+\frac23}}=1+\frac{1}{1+\frac{1}{\frac53}}=1+\frac{1}{1+\frac35}=1+\frac{1}{\frac85}=1+\frac58=1\frac58.$$

6) $$2-\frac{1}{2-\frac{1}{2-\frac{1}{2-\frac12}}}=2-\frac{1}{2-\frac{1}{2-\frac{1}{\frac32}}}=2-\frac{1}{2-\frac{1}{\frac43}}=2-\frac{1}{2-\frac34}=2-\frac{1}{\frac54}=2-\frac45=1\frac15.$$